Breast cancer mortality is declining in most high-income countries. The role of mammography screening in these declines is much debated. Screening impacts cancer mortality through decreasing the incidence of number of advanced cancers with poor prognosis, while therapies and patient management impact cancer mortality through decreasing the fatality of cancers. The effectiveness of cancer screening is the ability of a screening method to curb the incidence of advanced cancers in populations. Methods for evaluating cancer screening effectiveness are based on the monitoring of age-adjusted incidence rates of advanced cancers that should decrease after the introduction of screening. Likewise, cancer-specific mortality rates should decline more rapidly in areas with screening than in areas without or with lower levels of screening but where patient management is similar. These two criteria have provided evidence that screening for colorectal and cervical cancer contributes to decreasing the mortality associated with these two cancers. In contrast, screening for neuroblastoma in children was discontinued in the early 2000s because these two criteria were not met. In addition, overdiagnosis - i.e. the detection of non-progressing occult neuroblastoma that would not have been life-threatening during the subject's lifetime - is a major undesirable consequence of screening. Accumulating epidemiological data show that in populations where mammography screening has been widespread for a long time, there has been no or only a modest decline in the incidence of advanced cancers, including that of de novo metastatic (stage IV) cancers at diagnosis. Moreover, breast cancer mortality reductions are similar in areas with early introduction and high penetration of screening and in areas with late introduction and low penetration of screening. Overdiagnosis is commonplace, representing 20% or more of all breast cancers among women invited to screening and 30-50% of screen-detected cancers. Overdiagnosis leads to overtreatment and inflicts considerable physical, psychological and economic harm on many women. Overdiagnosis has also exerted considerable disruptive effects on the interpretation of clinical outcomes expressed in percentages (instead of rates) or as overall survival (instead of mortality rates or stage-specific survival). Rates of radical mastectomies have not decreased following the introduction of screening and keep rising in some countries (e.g. the United States of America (USA)). Hence, the epidemiological picture of mammography screening closely resembles that of screening for neuroblastoma. Reappraisals of Swedish mammography trials demonstrate that the design and statistical analysis of these trials were different from those of all trials on screening for cancers other than breast cancer. We found compelling indications that these trials overestimated reductions in breast cancer mortality associated with screening, in part because of the statistical analyses themselves, in part because of improved therapies and underreporting of breast cancer as the underlying cause of death in screening groups. In this regard, Swedish trials should publish the stage-specific breast cancer mortality rates for the screening and control groups separately. Results of the Greater New York Health Insurance Plan trial are biased because of the underreporting of breast cancer cases and deaths that occurred in women who did not participate in screening. After 17 years of follow-up, the United Kingdom (UK) Age Trial showed no benefit from mammography screening starting at age 39-41. Until around 2005, most proponents of breast screening backed the monitoring of changes in advanced cancer incidence and comparative studies on breast cancer mortality for the evaluation of breast screening effectiveness. However, in an attempt to mitigate the contradictions between results of mammography trials and population data, breast-screening proponents have elected to change the criteria for the evaluation of cancer screening effectiveness, giving precedence to incidence-based mortality (IBM) and case-control studies. But practically all IBM studies on mammography screening have a strong ecological component in their design. The two IBM studies done in Norway that meet all methodological requirements do not document significant reductions in breast cancer mortality associated with mammography screening. Because of their propensity to exaggerate the health benefits of screening, case-control studies may demonstrate that mammography screening could reduce the risk of death from diseases other than breast cancer. Numerous statistical model approaches have been conducted for estimating the contributions of screening and of patient management to reductions in breast cancer mortality. Unverified assumptions are needed for running these models. For instance, many models assume that if screening had not occurred, the majority of screen-detected asymptomatic cancers would have progressed to symptomatic advanced cancers. This assumption is not grounded in evidence because a large proportion of screen-detected breast cancers represent overdiagnosis and hence non-progressing tumours. The accumulation of population data in well-screened populations diminishes the relevance of model approaches. The comparison of the performance of different screening modalities - e.g. mammography, digital mammography, ultrasonography, magnetic resonance imaging (MRI), three-dimensional tomosynthesis (TDT) - concentrates on detection rates, which is the ability of a technique to detect more cancers than other techniques. However, a greater detection rate tells little about the capacity to prevent interval and advanced cancers and could just reflect additional overdiagnosis. Studies based on the incidence of advanced cancers and on the evaluation of overdiagnosis should be conducted before marketing new breast-imaging technologies. Women at high risk of breast cancer (i.e. 30% lifetime risk and more), such as women with BRCA1/2 mutations, require a close breast surveillance. MRI is the preferred imaging method until more radical risk-reduction options are eventually adopted. For women with an intermediate risk of breast cancer (i.e. 10-29% lifetime risk), including women with extremely dense breast at mammography, there is no evidence that more frequent mammography screening or screening with other modalities actually reduces the risk of breast cancer death. A plethora of epidemiological data shows that, since 1985, progress in the management of breast cancer patients has led to marked reductions in stage-specific breast cancer mortality, even for patients with disseminated disease (i.e. stage IV cancer) at diagnosis. In contrast, the epidemiological data point to a marginal contribution of mammography screening in the decline in breast cancer mortality. Moreover, the more effective the treatments, the less favourable are the harm-benefit balance of screening mammography. New, effective methods for breast screening are needed, as well as research on risk-based screening strategies.